Chaotic oscillations in a map-based model of neural activity

Abstract

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the phase plane, containing chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking etc.) derived from the proposed model.

References in corpus (4)

• Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map
• Regularization of Synchronized Chaotic Bursts
• Subthreshold oscillations in a map-based neuron model
• Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

Cited by in corpus (8)

• A Brief History of Excitable Map-Based Neurons and Neural Networks
• Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons
• Evolving dynamical networks with transient cluster activity
• Asymmetric coupling of nonchaotic Rulkov neurons: Fractal attractors, quasimultistability, and final state sensitivity
• Mean-field dynamics of a population of stochastic map neurons
• A generalized public goods game with coupling of individual ability and project benefit
• Chaotic Dynamics and Fractal Geometry in Ring Lattice Systems of Nonchaotic Rulkov Neurons
• Single-Entity Spiking Neuron Models: Survey